Supplementary Figure 1 Structure of InHCF. a, Selected-area electron diffraction pattern of individual InHCF nanocube (scale bar 5 nm -1 ). b and c, SEM and TEM image of InHCF/Gr (scale bar 100 nm). 1
Supplementary Figure 2 Cyclic voltammograms for InHCF/Gr in various electrolytes. Scan rate: 2 mv s -1. All scans start from the open circuit voltage (E ocp ) of the electrodes in electrolytes. Blue line is corresponding to 0.5 M Li 2 SO 4 in a and b; or 0.5 M K 2 SO 4 in c. Green line is corresponding to 0.25 M Li 2 SO 4 + 0.25 M Na 2 SO 4 in a; or 0.25 M Li 2 SO 4 + 0.25 M K 2 SO 4 in b; or 0.25 M Na 2 SO 4 + 0.25 M K 2 SO 4 in c. Red line is corresponding to 0.1 M Li 2 SO 4 + 0.4 M Na 2 SO 4 in a; or 0.1 M Li 2 SO 4 + 0.4 M K 2 SO 4 in b; or 0.4 M Na 2 SO 4 + 0.1 M K 2 SO 4 in c. Black line is corresponding to 0.5 M Na 2 SO 4 in a and c; or 0.5 M K 2 SO 4 in b. The E ocp of the electrodes in a, b and c follow the same order: black > red > green > blue. E ocp, the open circuit potential of the as-prepared electrode in the electrolytes that is an important indicator of the chemical sates. From the E ocp, we can see that InHCF/Gr is a compound with oxidation form. 2
3
Supplementary Figure 3 Comparison of rate capability between InHCF/Gr and InHCF. Rate capabilities of InHCF/Gr (a, c, e) and InHCF (b, d, f) in aqueous 0.5 M Li 2 SO 4 (a, b), 0.5 M Na 2 SO 4 (c, d) and 0.5 M K 2 SO 4 (e, f). g is the summary of rate capabilities of InHCF/Gr and InHCF in different electrolytes (C s is the specific discharging capacity, and percentage is the normalized discharging capacity which is compared with the discharging capacity measured at 1C rate). E (V) is normalized to SHE, and 1C equals to 60 ma g -1. 4
Supplementary Figure 4 Plots of E f, E ocp and E 1/2 vs. the composition of mixed-ion electrolytes. a, Li + /Na + mixed-ion electrolytes; b, Li + /K + mixed-ion electrolytes; c, Na + /K + mixed-ion electrolytes. E f, formal potential, the average of the anode and cathode peak potentials (E pa and E pc ); E ocp, the open circuit potential of the as-prepared electrode in the electrolytes that is an important indicator of the chemical sates; E 1/2, the voltage that is measured when the electrode material has discharged 50% of its total capacity at a rate of 1C. 5
Supplementary Figure 5 Rate capabilities of InHCF/Gr in various electrolytes. Rate capabilities of InHCF/Gr in aqueous 0.25 M Li 2 SO 4 +0.25 M Na 2 SO 4 (a), 0.1 M Li 2 SO 4 +0.4 M Na 2 SO 4 (b), 0.25 M Li 2 SO 4 +0.25 M K 2 SO 4 (c), 0.1 M Li 2 SO 4 +0.4 M K 2 SO 4 (d), 0.4 M Na 2 SO 4 +0.1 M K 2 SO 4 (e), and 0.25 M Na 2 SO 4 +0.25 M K 2 SO 4 (f). E (V) is normalized to SHE, and 1C equals to 60 ma g -1. 6
Supplementary Figure 6 Summary of rate capabilities of InHCF/Gr in various mixed-ion electrolytes. a, Li + /Na + mixed-ion electrolytes; b, Li + /K + mixed-ion electrolytes; c, Na + /K + mixed-ion electrolytes. C s is the specific discharging capacity, and percentage is the normalized discharging capacity which is compared with the discharging capacity measured at 1C rate. 1C = 60 ma g -1. 7
Supplementary Figure 7 Cubic TiP 2 O 7. a, crystal structure of cubic TiP 2 O 7 with space group Pa3. b, Rietveld refinement of X-ray power diffraction pattern for carbon-coated TiP 2 O 7. c, TGA curves of carbon-coated TiP 2 O 7. d, SEM images of carbon-coated TiP 2 O 7 with different magnification. Scale bar 400 nm. e, TEM image of TiP 2 O 7 nanoparticles (upper left), high-resolution TEM image of selected section marked by red rectangle (right) and its corresponding FFT pattern (lower left). Scale bar 10 nm. 8
Supplementary Figure 8 Rhombohedral NaTi 2 (PO 4 ) 3. a, crystal structure of rhombohedral NaTi 2 (PO 4 ) 3 with space group R-3c. b, Rietveld refinement of X-ray power diffraction pattern for carbon-coated NaTi 2 (PO 4 ) 3. c, TGA curves of carbon-coated NaTi 2 (PO 4 ) 3. d, SEM images of carbon-coated TiP 2 O 7 with different magnification. Scale bar 400 nm. e, TEM image of NaTi 2 (PO 4 ) 3 nanoparticles (upper left), high-resolution TEM image of selected section marked by red rectangle (right), and its corresponding FFT pattern (lower left). Scale bar 10 nm. 9
Supplementary Figure 9 Cyclic voltammograms at a scan rate of 0.3 mv s -1 for carbon-coated NaTi 2 (PO 4 ) 3 in 0.5 M Na 2 SO 4 (initial 5 cycles). All electrode potentials are vs. standard hydrogen electrode (SHE). 10
Supplementary Figure 10 Rate capabilities of InHCF+Gr. a, discharging curves of InHCF+Gr in 0.5 M Li 2 SO 4 at various rates. b, comparison of rate capabilities of InHCF/Gr, InHCF, InHCF+Gr in 0.5 M Li 2 SO 4. (InHCF+Gr is the physical mixture of InHCF and graphene with the mass ratio of 10:1, C s is the specific discharging capacity, and percentage is the normalized discharging capacity which is compared with the discharging capacity measured at 1C rate). E (V) is normalized to SHE, and 1C equals 60 ma g -1. 11
Supplementary Figure 11 Ex-situ XPS spectra recorded from F 1s and N 1s core level of InHCF/Gr at different charging/discharging states. The explanations of different states are illustrated in the caption of Figure 5 in the manuscript. 12
Supplementary Figure 12 Volume of InHCF formula unit after A + (Li +, Na + and K + ) occupying five different sites. The dashed line is the volume of InHCF formula unit with empty A + (299.4 Å 3 ). The most stable interstitial sites (24d sites for Li + and Na + ; 48g site for K + ) are marked by the solid symbols. 13
Supplementary Figure 13 Crystal structures of InHCF with intercalation of H 2 O. Green ball: Fe; blue ball: In; orange ball: C; wine ball: N; red ball: O; pink ball: H. 14
Supplementary Figure 14 Geometries of solvated alkali cations (from 2-coordination to 4-coordination) determined by DFT calculations. [A(H 2 O) 2 ] +, [A(H 3 O) 2 ] + and [A(H 3 O) 4 ] + prefer linear, triangular and tetrahedral structure, respectively. 15
Supplementary Figure 15 Electronic density of states projected on In atom in InHCF (top), NaInHCF (middle) and NaInHCF-H 2 O (bottom). 16
Supplementary Table 1. Structural parameter of InHCF in the Fm-3m structure determined from Rietveld method using powder X-ray diffraction data (Rietveld) and ab initio calculations with the GGA+U approximation (GGA+U). Structural parameters Rietveld Value GGA+U Lattice parameter a = b = c 10.51 Å 10.62 Å α = β = γ 90 o 90 o Bond distance Fe-C 1.97 Å 1.91 Å In-N 2.13 Å 2.23 Å C-N 1.15 Å 1.17 Å Angle In-N-C 180 o 180 o Fe-C-N 180 o 180 o 17
Supplementary Table 2. Fractional coordinates of Fe, In, C and N of InHCF in the Fm-3m structure determined from Rietveld method using powder X-ray diffraction data (Rietveld) and ab initio calculations with the GGA+U approximation (GGA+U). Atom Wyckoff position Method x y z Site occupancy Fe In C N 4a 4b 24e 24e Rietveld 0 0 0 1 GGA+U 0 0 0 1 Rietveld 0.5 0.5 0.5 1 GGA+U 0.5 0.5 0.5 1 Rietveld 0.1795 0 0 1 GGA+U 0.1878 0 0 1 Rietveld 0.2896 0 0 1 GGA+U 0.2972 0 0 1 18
Supplementary Table 3. Energy densities & average operating voltagesof various RAMB. Energy density is calculated based on the total mass of active electrode materials. RAMB type (cathode/anode) Average operating voltage / V Aqueous Lithium-ion Batteries Energy density Capacity retention / Wh kg -1 / % (cycle no.) Reference LiMn 2 O 4 /VO 2 1.5 55 Failed (25) [1] LiMn 2 O 4 /LiTi 2 (PO 4 ) 3 1.5 60 85 (50) [2] LiMn 2 O 4 /TiP 2 O 7 1.4 59 37 (25) [3] LiMn 2 O 4 /LiV 3 O 8 1.0 55 54 (100) [4] LiFePO 4 /LiTi 2 (PO 4 ) 3 0.9 50 90 (1000) [5] LiCoO 2 /LiV 3 O 8 1.0 35 36 (100) [6] LiNi 0.81 Co 0.19 O 2 /LiV 3 O 8 LiMn 2 O 4 /Mo 6 S 8 1.1 1.7~1.8 50 84 70 (30) 78 (100) InHCF/TiP 2 O 7 1.2 41 n.a. This work Aqueous Sodium-ion and Potassium-ion Batteries Na 0.44 MnO 2 /NaTi 2 (PO 4 ) 3 1.1 33 60 (700) [9] Na 0.44 MnO 2 /AC 0.9 < 40 90 (1000) [10] Na 0.44 [Mn 0.66 Ti 0.34 ]O 2 /NaTi 2 (PO 4 ) 3 < 1.2 not shown 89 (300) [11] Na 0.44 [Mn 0.44 Ti 0.56 ]O 2 /NaTi 2 (PO 4 ) 3 1.1 not shown n.a. [11], [12] Na 2 NiFe(CN) 6 /NaTi 2 (PO 4 ) 3 1.27 43 88 (250) [13] Na 2 CuFe(CN) 6 /NaTi 2 (PO 4 ) 3 1.4 48 90 (1000) [14] Na 2 CoFe(CN) 6 /NaTi 2 (PO 4 ) 3 1 (1.7 and 0.4) 67 90 (800) [15] K 0.27 MnO 2 /NaTi 2 (PO 4 ) 3 0.8 not shown n.a. [16] Na 2 CuFe(CN) 6 /NaMn 2 (CN) 6 0.95 27 > 90 (1000) [17] KCuFe(CN) 6 /Ppy CoCuHCF/SNDI 0.9 < 1.1 V 5 26 > 90 (1000) 86 (100) InHCF/NaTi 2 (PO 4 ) 3 1.55 54 n.a. This work Aqueous Mixed-ion Batteries LiMn 2 O 4 /Na 0.22 MnO 2 (Li + /Na + ) 0.6 21 83 (45) Our group, [20] Na 0.44 MnO 2 /TiP 2 O 7 (Li + /Na + ) 1.05 40 62 (50) Our group, [20] Ni 1 Zn 1 HCF/TiP 2 O 7 (Li + /K + ) 1.25 46 63 (50) Our group, [21] Ni 1 Zn 1 HCF/NaTi 2 (PO 4 ) 3 (Na + /K + ) 1.45 53 49 (50) Our group, [21] InHCF/TiP 2 O 7 (Li + /Na + ) 1.45 49 n.a. This work InHCF/TiP 2 O 7 (Li + /K + ) 1.40 48 n.a. This work InHCF/NaTi 2 (PO 4 ) 3 (Na + /K + ) 1.60 56 90 (200) This work LiMn 2 O 4 /Zn (Li + /Zn 2+ ) 1.7~1.8 50~80 95 (4000) [22] LiFePO 4 /Zn (Li + /Zn 2+ ) 1.2 not shown > 90 (100) [22],[23] Na 0.95 MnO 2 /Zn (Na + /Zn 2+ ) 1.5 78 92 (1000) [24] Aqueous Zinc-ion Batteries α-mno 2 /Zn 1.3 not shown 78 (100) [25] ZnHCF/Zn CuHCF/Zn 1.7 1.7 100 not shown 81 (100) 96 (100) [7] [8] [18] [19] Our group, [26] [27] 19
Supplementary Table 4. Coulombic efficiency (CE) of InHCF/Na + +K + /NaTi 2 (PO 4 ) 3 battery with cycles. Cycle CE/100% Cycle CE/100% Cycle CE/100% Cycle CE/100% no. no. no. no. 1 96.6 45 99.3 100 99.4 155 99.6 2 98.1 50 99.3 105 99.2 160 99.2 3 98.9 55 99.6 110 99.4 165 99.4 5 99.3 60 99.3 115 99.5 170 99.2 10 99.4 65 98.9 120 98.1 175 99 15 99.5 70 99.4 125 99.3 180 99.5 20 98.5 75 99.4 130 99.3 185 99.2 25 99.5 80 98.5 135 99.6 190 99.5 30 99.5 85 99.4 140 99.4 195 99.2 35 99.3 90 99.4 145 99.2 200 99.4 40 98.7 95 99.5 150 99.3 20
Supplementary Table 5. Atomic concentration of different elements in InHCF/Gr during electrochemical cycling which are determined by XPS. States Atomic concentration / % Na Fe N In a 7.84 10.15 68.86 13.15 b 5.39 11.40 70.62 12.59 c 4.29 10.73 71.14 13.84 d 3.12 12.09 71.23 13.56 e 6.37 10.64 69.50 13.49 f 7.22 11.45 67.32 14.01 g 7.72 10.00 69.44 12.84 21
Supplementary Note 1: the equal specific capacity of InHCF/Gr with Li +, Na + and K +. Our InHCF/Gr is a cation-deficient (oxidation form) compound (see Supplementary Figure 2). An A + -intercalation reaction that occurs at InHCF can be written as follows: InHCF (Ox) + na + (Aq) + ne A n InHCF (Red) It can be seen that InHCF (Ox) has the same molecular weight and A n InHCF (Red) has different molecular weights with different A +. Due to its same molecular weight, the specific discharging capacities of InHCF/Gr (oxidation form) with Li +, Na + and K + are the same. 22
Supplementary Note 2: the coulombic efficiency and voltage charge limits of InHCF/Na + +K + /NaTi 2 (PO 4 ) 3 battery. From the Supplementary Table 4, we can see that the coulombic efficiency is almost above 99 % at each cycle except some occasional cycles (e.g., 1th, 2th, 3th, 20 th, 65th, 80th, 120 th.). So it is concluded that many side reactions (e.g., water electrolysis reactions) are eliminated during cycling despite the high voltage charge limit (1.83 V) for aqueous electrolytes. Electrolysis of pure water into H 2 and O 2 at 298 K can be written as following Nernst equations: O 2 evolution: 2H 2 O (l) O 2 (g) + 4H + (aq) + 4e o E red = 1.23 V vs. SHE o E(O 2 ) = E red 4RTln[H + ]/4F = 1.23 0.059pH H 2 evolution: 2H + (aq) + 2e o H 2 (g) E red = 0 V vs. SHE o E(H 2 ) = E red 2RTln[H + ]/2F = 0 0.059pH So it can be seen that the reaction potentials of O 2 and H 2 evolution are ph-dependent. At ph = 7.0, the theoretical reaction potentials of O 2 and H 2 evolution are 0.82 V and 0.41 V vs. SHE, respectively. Our mixed-ion electrolytes as well as aqueous Li 2 SO 4, Na 2 SO 4 and K 2 SO 4 are neutral electrolytes (ph = 7.0). For the mixed-ion batteries as shown in Figure 3 of the manuscript, the cut-off charging voltage for InHCF/Gr cathode is 1.2 V vs. SHE that is beyond 0.82 V. In terms of TiP 2 O 7 and NaTi 2 (PO 4 ) 3 anodes, their cut-off discharging voltages are 0.56 V and 0.65 V vs. SHE, respectively, which are lower than theoretical reaction potential of H 2 evolution ( 0.41 V vs. SHE). Although the cut-off voltage limits for InHCF/Gr, TiP 2 O 7 and NaTi 2 (PO 4 ) 3 are beyond the theoretical reaction potentials of H 2 /O 2 evolution, their coulombic efficiency are around 100% (see Figure 3 of the manuscript), suggesting that water electrolysis reactions (both H 2 and O 2 evolution) are negligible. The electrolytes solutions before and after cycling have been analyzed by ICP-OES. It is found that after cycling, the total concentration of M + and N + of the electrolytes is 1.04 ± 0.01 M, almost the same as the one before cycling (1.01 ± 0.01 M). 23
Supplementary Note 3: the fading mechanism of InHCF/Na + +K + /NaTi 2 (PO 4 ) 3 battery. Our previous studies and other groups have found that oxygen that could react with the discharged-stated anode electrode materials is the primary cause of the capacity fading upon cycling. Although our used electrolytes here are all deaerated solution, we found that TiP 2 O 7 and NaTi 2 (PO 4 ) 3 undergo very slight fading upon cycling in deaerated solution (see Supplementary Figure 9). It could be attributed to the trace of oxygen in the electrolytes. We also found that InHCF/Gr exhibits excellent cycle life (no obvious decaying is observed). So the fading of InHCF/Na + +K + /NaTi 2 (PO 4 ) 3 battery mainly comes from the NaTi 2 (PO 4 ) 3 anode. 24
Supplementary Note 4: the role of graphene. In our InHCF/Gr, the mass ratio between InHCF and graphene is about 10:1. We choose the physical mixture of InHCF and graphene (InHCF+Gr) to study the effect of graphene on the rate performance of InHCF. In InHCF+Gr, the mass ratio of InHCF and graphene is also fixed at 10:1. Supplementary Figure 10 shows that discharging curves of InHCF+Gr at various rates in 0.5 M Li 2 SO 4. As shown, InHCF+Gr at various rates exhibits higher capacity retention than InHCF, indicating that graphene serves as a 3D electronic network to diminish the resistance between InHCF nanoparticles, which facilitates the electron transfer. And InHCF/Gr shows slightly higher capacity retention than InHCF+Gr. It can be explained by the fact that the average size of InHCF/Gr is smaller than that of InHCF (see the manuscript). The reason is that 2D graphene adsorbs InHCF nanocrystals during the nucleation stage of precipitation reaction, which blocks their further growth up. Similar electrochemical results are also found in Na 2 SO 4, K 2 SO 4, and mixed-ion electrolytes. So it is concluded that graphene not only acts as a moderator during nucleation, but also serves as an electronic network. 25
Supplementary Note 5: the role of mixed-ion electrolytes. Our previous studies [20, 21] have shown that cubic TiP 2 O 7 and rhombohedral NaTi 2 (PO 4 ) 3 can be used as the anodes for AMIB, as a result of their specific ion-selectivity properties (TiP 2 O 7, ion-selectivity toward Li + against Na + and K + ; NaTi 2 (PO 4 ) 3, ion-selectivity toward Na + against K + ) and reasonable working voltages. When an intercalation reaction occurs at H with ion-selectivity towards A + as shown in equation (1), the reaction potential (E) can be calculated using the Nernst equation (2): H (s) + na + (aq) + ne A n H (s) (1) E = E Θ + 2.303RT lg(a n nf A + a H a An H) (2) where a A +, a H and a An H refer to the activities of A +, H and A + -intercalated H (A n H). As the total concentration of M + and N + in our mixed-electrolytes is fixed at 1 M to ensure the equal conductivity of the electrolytes, the activity of a given cation in mixed-electrolytes (here we briefly consider it as the concentration of the cation) is below 1 M. Our previous electrochemical data have shown that E for TiP 2 O 7 decrease with decreasing the Li + /Na + or Li + /K + ratio in mixed-electrolytes ([Li + ] + [Na + ] = 1 M and [Li + ] + [K + ] = 1 M), and E for NaTi 2 (PO 4 ) 3 decrease with decreasing the Na/K + ratio in mixed-electrolytes ([Na + ] + [K + ] = 1 M) [20, 21]. Therefore, equations (1) and (2) are valid for the electrode materials with ion-selectivity property. In terms of electrode materials that allow for co-intercalation of two alkali cations such as InHCF, these equations are not valid. The CV data in our previous paper have also show that Li + (not Na + and K + ) can be intercalated into TiP 2 O 7, and Na + (not K + ) can be intercalated into NaTi 2 (PO 4 ) 3 [20, 21]. The ion-selective properties of above TiP 2 O 7 and NaTi 2 (PO 4 ) 3 can be easily explained by the steric effect: Na + and K + are too large to enter into TiP 2 O 7 three-dimensional framework while K + is also too large for NaTi 2 (PO 4 ) 3. For AMIB, one important characteristic is that the total concentration of M + and N + in the electrolytes is fixed during charging/discharging, but the M + /N + ratio is changed. We have demonstrated this point in the paper [20]. From our previous [20, 21] and current studies, the A + -intercalation voltages for TiP 2 O 7 and NaTi 2 (PO 4 ) 3 (anode materials) are decreased by 40 ~ 50 mv when using mixed cations as electrolytes instead of single cation. Here, the working voltages of InHCF/Gr (cathode material) are increased by 200 mv (Li + /Na + ) and 150 mv (Li + /K + ) in the mixed electrolytes when compared to electrolytes containing only Li +. So compared to InHCF/Li + /TiP 2 O 7 battery, the increases of voltage output for InHCF/Li + +Na + /TiP 2 O 7 (250 mv) and InHCF/Li + +K + /TiP 2 O 7 (200 mv) batteries are mainly from the InHCF cathode. The working voltage of InHCF/Gr in Na + /K + -mixed electrolytes is almost identical to the one in Na 2 SO 4. When compared to InHCF/Na + /NaTi 2 (PO 4 ) 3 battery, the slight increase of voltage output (ca. 50 mv) for InHCF/Na + +K + /NaTi 2 (PO 4 ) 3 battery comes from the NaTi 2 (PO 4 ) 3 anode. 26
Supplementary Note 6: water-mediated cation intercalation of InHCF. Depending on the number of co-ordinated water, [A(H 2 O) n ] + solvated ions has different geometries. Supplementary Figure 14 displays the geometries of solvated ions (from 2-coordination to 4-coordination) determined by DFT calculations. As shown, [A(H 2 O) 2 ] +, [A(H 3 O) 3 ] + and [A(H 3 O) 4 ] + prefer linear, triangular and tetrahedral structure, respectively. The bond distances of Li-O, Na-O and K-O are 1.9 Å, 2.2 Å and 2.7 Å, respectively, which are very close to the experimental values (2.0 Å, 2.3 Å and 2.7 Å) in reference [Marcus, Y. Chem. Rev. 88, 1475 1498 (1988).]. When [Li-OH 2 ] + or [Na-OH 2 ] + is intercalated into InHCF, the bond distance of Li-O or Na-O in InHCF is 1.88 Å (or 2.24 Å), similar to the one in [A(H 2 O) n ] + solvated ions. Meanwhile, the sizes of all solvated ions (from 2-coordination to 4-coordination) shown in the Supplementary Figure 14 are estimated to be above 5.2 Å. In the cubic structure of InHCF as shown in Fig. 6a of the manuscript, A + can occupy five possible interstitial sites. Among them, 8c site provides the largest free space. To avoid significant expansion of the lattice framework, the radius of guest ion to occupy the 8c site should be limited to 260 pm. So it is concluded that above solvated ions as well as [K-OH 2 ] + (radius 288 pm) can not be intercalated into InHCF. 27
Supplementary Methods DFT calculation. During the charging and discharging of an alkali-ion battery, an alkali A + is inserted or extracted from a host crystal structure A n H. For a battery that operates by shuttling A + ions between the cathode and a pure alkali metal anode, the overall cell reaction can be written as follows: H (s) + na (s) A n H (s) (1) The forward reaction is the cell discharging reaction, while the reverse is the cell charging reaction. The average intercalation potential V vs. A/A + can then be calculated using the following equation [28, 29]: = = (A n H) (H) n (A) n n Where E b is the binding energy between A + ion and H, E(A n H), E(H) and E(A) are the total energies of A n H, H and metallic A which are calculated using DFT, and e is the absolute value of the electron charge. In aqueous alkali-ion battery, m/n H 2 O accompany the insertion and extraction of one A + during entire charge and discharge process. So the overall cell reaction can be written by equation (3): H (s) + na (s) + mh 2 O A n (H 2 O) m H (s) (3) (2) The average intercalation potential V vs. A/A + equation: can then be calculated using the following = = (A n(h ) H) (H) n (A) (H ) n n Where E b is the binding energy between [A-(OH 2 ) m/n ] + ion and H, E(A n (H 2 O) m H) and E(H 2 O) are the total energies of A n (H 2 O) m H and water which are calculated using DFT. In this work, we employ m = n = 1 to calculate the average intercalation potential and E b for [Li-OH 2 ] + and [Na-OH 2 ] +, and m = 1, n = 0 to calculate E b for H 2 O. The calculated energies of InHCF, metallic Li, Na, K and H 2 O are as follows: E(InHCF) = 108.71 ev; E(Li) 1.89 ev; E(Na) 1.30 ev; E(K) 1.04 ev; E(H 2 O) = 14.22 ev. (4) 28
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